Preparation and Heat Dissipation Properties Comparison of Al and Cu Foam

Abstract

The space holder method, a kind of powder metallurgy method which can avoid the process of melting metal to prepare metal foams, has particular significance in solving the difficulty of preparing metal foams with high melting points. In this paper, Na₂S₂O₃·5H₂O, a novel space holder, was used to prepare aluminium foam and copper foam, which were then used to test the heat dissipation performance of the metal foams. We first prepared two kinds of cell structures for (spherical cell and composite cells) aluminium and copper foam, then, we compared the performances of their heat dissipation, and it was found that both the spherical cell metal foam and composite cell metal foam promoted heat dissipation in the environment of natural convection, and the difference between them was not apparent. In the environment of forced convection, the composite porous metal showed a better heat dissipation performance.

1. Introduction

Metal foam is a unique metal and a porous material, and it is similar to sponge structures. Metal foam has a series of excellent properties, such as a low mass, a high strength [1], good thermal insulation [2], good sound insulation [3], a good electromagnetic shielding performance [4], etc. Therefore, the metal foam has received widespread attention at home and abroad.

There are also various methods that are used for preparing metal foams which can be classified as casting methods [5,6,7], sintering methods [8,9], deposition methods [10,11,12], de-alloying methods [13,14], and high energy beam rapid prototyping [15,16]. However, for the preparation of high melting point metal foams, the casting method has a certain risk, which is that the porosity is not controllable, the deposition method has a high cost, and the metal foam prepared by the de-alloying method has a small cell size usually. For the high-energy beam rapid prototyping method, though it can prepare porous materials with arbitrary cell shapes, its cost is high. Therefore, considering the safety, cell controllability, and cost, the space holder method in the powder metallurgic was selected to prepare metal foam with high porosity in this paper.

For the selection of space holder, Hasan et al. [17,18] studied aluminium foam with 40%–85% porosity which had been prepared by the powder sintering of aluminium powder and urea. They found out the addition of 1 wt% magnesium and 1 wt% tin powder leads to liquid phase sintering, and it produces a dense aluminium matrix with higher mechanical properties. Yoshihiko et al. [19] successfully fabricated Cu foam specimens with porosities of 60–80% by the friction powder compaction process. In addition, it has been proved that the plateau stress and energy absorption decrease with increasing porosity, indicating the strong relationship between them. The Cu foam with the highest energy absorption per unit volume changed from a high-porosity Cu foam to a low-porosity Cu foam with increasing compression stress. Consequently, the mechanical properties of Cu foam can be controlled by adjusting the volume fraction of NaCl. Amit et al. [20] successfully prepared Ti₂Co alloy foam using NH₄HCO₃ as the space holder. They concluded that the relative density of Ti₂Co foam decreases with an increase in the space holder content, but it increases marginally with Al contents. Additionally, the plateau stress, energy absorption and elastic modulus of the foams increased with the Al content and relative density. These foam properties follow the power law relation with relative density. Leilei Sun et al. [21] used a novel space holder, Na₂S₂O₃·5H₂O, to prepare structurally controlled aluminium foam. According to this paper, it is important to know that Na₂S₂O₃·5H₂O is easy to dissolve in water and it has a high hardness and low melting point. In addition, it can reshape the shape and size of the space holder. In this paper, Na₂S₂O₃·5H₂O was selected as the space holder, and it was made into reticulated hexagonal channels and spherical structures of different sizes, resulting in aluminium and copper foam with spherical and composite cells.

In terms of the thermal performance, T.S. Athith et al. [22] dealt with the numerical simulations of a heat exchanger that was partially filled with three different metal foams made of Aluminium (Al), Copper (Cu) and Nickel (Ni) with two cell densities, namely, 20 PPI and 40 PPI, respectively. From the numerical simulations, it was observed that there is a 5.68 times enhancement in the heat transfer rate when the copper foam was used for higher inlet velocities in comparison with the that of non-porous channel. Limei Shen et al. [23] applied metal foam to the heat pipe radiator, which combined with the aluminium substrate, the copper foam, and the heat pipe. Furthermore, it was proved by the experiment that the metal foam heat pipe radiator is more suitable for compact cooling systems due to its lighter weight, lower power consumption, and higher dissipation performance.

In this paper, the structural analyses of aluminium and copper foam with two kinds of cell structures were carried out, and the thermal performance of the aluminium and copper foam was tested. Finally, the heat dissipation results were summarized, and the performance was analyzed.

2. Experiment

The materials used in this experiment were aluminium powder with a particle size of 50 μm, copper powder with a particle size of 50 μm, and Na₂S₂O₃·5H₂O which was used as the space holder for the preparation of the aluminium and copper foam. In addition, the experimental materials used for the heat dissipation tests include a copper block with a size of 40 mm × 40 mm × 20mm and weight of about 300 g, a power switch transformer with an output power of 24 V, a digital display temperature controller, a silica gel heating sheet, a fan, an acrylic glass sheet, asbestos, and thermal silicone grease.

Figure 1 is a flow chart of the preparation of the metal foams using Na₂S₂O₃·5H₂O as the space holder. The method of preparing a specifically shaped space holder in this paper is consistent with Leilei Sun’s one [21]. According to this paper, an ABS plastic mould made using 3D printing technology was used to shape them into a semi-transparent silica gel moulds to prepare the Na₂S₂O₃·5H₂O particles. Differently from the references, the hexagonal channels were prepared in this paper. The size of the space holder prepared in this paper is shown in Figure 2.

The experiment aimed to prepare aluminium and copper foam with about 70% porosity. During the process of preparation, we used the ratio of the components shown in

Table 1. The ratio of the components.

(a) Aluminium foam
Category	The Mass of Powder/g	The Mass of Na2S2O3·5H2O/g	The Mass of the Hexagonal Mesh/Piece
Spherical cell	32.28	48.38	/
Composite cell	26.98	40.32	11
(b) Copper foam
Category	The Mass of Powder/g	The Mass of Na2S2O3·5H2O/g	The Mass of the Hexagonal Mesh/Piece
Spherical cell	107.51	48.41	/
Composite cell	89.59	40.32	11

and the temperature rise curve of the aluminium and copper foam shown in Figure 3. In this paper, the prepared aluminium foam and copper foam contain two kinds of cell structure—spherical cells and composite cells. The spherical cell structure contains only a spherical structure, while the composite cells have both a hexagonal mesh structure and a spherical structure. In addition, attention should be paid to the preparation of the copper foam, and it has been verified by the experiments that using electrolytic copper powder or bathing it in hot water will cause the copper block to collapse, as shown in Figure 4, so the copper foam should be prepared with flake copper powder and a cold water bath, however, in the preparing process of aluminium foam, the water temperature should be 80 °C because it had been verified by the experiments that Na₂S₂O₃·5H₂O is more thoroughly dissolved at this temperature. It should be noted that the composition of the composite cells metal foams is uniform by controlling the quality of the mixed powder between the layers. For the aluminium foam, firstly, we put in 8 g of mixed powder, then, we added a hexagonal channel, then, 5 g of mixed powder and a hexagonal channel, and so on, until all 11 hexagonal channels had been added. For the copper foam, similar to the above method, the difference is that the weight of the mixed powder is 15.74 g for the first and last addition and 9.84 g for the intermediate addition. For the convenience of testing the heat dissipation performance, the prepared metal foam was cut into blocks with 25 mm squares which was initially a cylinder with a diameter of 40 mm and a height of 30 mm. The resulting metal foam is shown in Figure 5. Moreover, the diameter, the height, and the mass of the foam metal could be measured. The formula for calculating the porosity of the obtained sample is shown in the following Formulas (1)–(4):

$$V=L_M{}^2{h}_M$$

(1)

$$V_B=\frac{m_M}{{\rho }_B}$$

(2)

$$V_C=V-V_B$$

(3)

$$p=\frac{V_C}{V}$$

(4)

where $L_M$ is the measured length, mm; $h_M$ is the measured height, mm; $V$ is the total volume of the metal foam, mm³; $m_M$ is the measured mass, mm; ${\rho }_B$ is the density of the base material, g/mm³; $V_B$ is the volume of the base material, mm³; $V_C$ is the volume of the cells, mm³; $p$ is the porosity.

Moreover, the corresponding actual porosity is shown in

Table 2. Actual porosity $p$ of foam samples.

* Sample Number	${\mathit{L}}_{\mathit{M}}/\mathbf{mm}$	${\mathit{h}}_{\mathit{M}}/\mathbf{mm}$	V/cm3	${\mathit{m}}_{\mathit{M}}/\mathbf{g}$	${\mathit{V}}_{\mathit{B}}/{\mathbf{cm}}^3$	${\mathit{V}}_{\mathit{C}}/{\mathbf{cm}}^3$	$\mathit{p}/\%$
① (Al)	25	30.92	19.33	15.7	6.23	13.10	67.76
② (Al)	25	30.56	19.10	15.8	6.27	12.83	67.17
③ (Al)	25	30.75	19.22	15.6	6.19	13.03	67.79
④ (Al)	25	34.42	21.51	11.4	4.52	16.99	78.99
① (Cu)	25	30.5	19.06	51.7	6.18	12.88	67.55
② (Cu)	25	31	19.38	52.4	6.27	13.11	67.64
③ (Cu)	25	31	19.38	50.7	6.06	13.32	68.73
④ (Cu)	25	37	23.13	41.8	5.00	18.13	78.38

* Sample Number ①, ②, ③, and ④ are the same; Al refers to aluminium foam; Cu refers to copper foam.

.

The equipment used to the test heat dissipation performance is shown as follows. Moreover, the experiment was carried out at room temperature.

The natural convection device is shown in Figure 6, in which the copper block was placed on the silica gel heating plate, connected with thermal silicone grease, and surrounded by asbestos. During the operation, one thermostat worked, and its thermocouple was placed at the bottom of the silica gel heating sheet, and the other thermostat was only used to measure the temperature, and this was placed on the upper surface of the copper block.

Firstly, the copper block was heated to a specific temperature, and the initial temperatures were recorded. Then, the values of T1 and T2 in the cooling process were recorded to judge the heat dissipation performance. As the experiment went on, the T1 and T2 decreased. In addition, a control group was designed, and no metal foam block was placed.

For the forced convection test, the heat dissipation device was similar to the natural convection heat dissipation device, and we only increased the size of the air supply equipment and a section of the acrylic glass plate bonding pipe so that air flowed through the metal foam. Additionally, the rate of the air was 3.7 m/s. When we were placing the metal foam block, the sides and top of the metal foam were wrapped with asbestos, which was used to isolate the convective heat dissipation of the foam aluminium and reduce the system error. The device is shown in Figure 7.

When we were testing its forced convection heat dissipation performance, the T1 and T2 increased to a specific value. Then, we recorded the value, and the air from the fan removed the heat from the system. A group of experiments without metal foam were also conducted as the control group.

3. Results

3.1. The Results of Natural Convection Heat Dissipation

The heat dissipation results are shown in Figure 8. In the picture, the temperature gradient is a physical quantity that can reflect the speed of the heat dissipation. The temperature gradient is calculated by the Formula (5):

$$\mathrm{Grad}T=\underset{\Delta n\to 0}{\lim }(\frac{\Delta T}{\Delta n})\overrightarrow{n}=\frac{\partial T}{\partial n}\overrightarrow{n}$$

(5)

where n is a unit vector in the normal direction and it is the temperature derivative in the n direction.

In addition, the heat dissipation efficiency can be calculated. The formula is shown the Formula (6):

$$\eta =\frac{\Delta T_2}{\Delta T}\ast 100\%$$

(6)

where η is the heat dissipation efficiency, which means how fast it dissipates the heat indifferent conditions compared to the control group; $\Delta T_2$ is the drop in temperature of the metal foam; $\Delta T$ is the drop in temperature of the control group.

Under the natural convection condition, the temperature of the control group decreased by 23 °C, the spherical cell aluminium foam decreased by about 31.8 °C, and the temperature of the aluminium foam, which have two kinds of cell structures, decreased by about 31.7 °C. Compared with the control group, the heat dissipation efficiency of the spherical cell aluminium foam increased by 38.2%. In comparison, the composite cells aluminium foam increased by 37.8%, which is basically the same as that of the spherical cell.

For the copper foam, the temperature of the control group decreased by 23.7 °C, the spherical cell copper foam decreased by about 30.8 °C, and the temperature of the copper foam, which have two kinds of cell structures, decreased by about 32.8 °C. In the same way, heat dissipation efficiency can be calculated. The spherical and composite cells copper foam increased by 30.0% and 38.4%, respectively, compared with the control group.

It is not hard to see that metal foam had advantages in heat dissipation, and the copper foam lost heat slightly faster than the aluminium foam did under natural convection conditions. However, the composite pore structure does not show a superior heat dissipation performance in this case.

3.2. The Results of Forced Convection Heat Dissipation

The test results are shown in Figure 9.

It can be obviously seen that under the forced convection environment, the temperature of the control group decreased by about 26 °C, the temperature of the spherical cell aluminium foam decreased by about 33 °C, and the temperature of the composite cells aluminium foam decreased by about 44 °C. Compared with the control group, the heat dissipation efficiency of the spherical cell aluminium foam increased by 27%, while the composite cells aluminium foam increased by 69%.

However, when we tested the copper foam, the control group decreased by 25 °C, the spherical cell decreased by about 35 °C, the composite cells decreased by about 50 °C. The heat dissipation efficiency of the spherical cell copper foam increases by 35%, and that of composite cells copper foam increased by 92%.

It was found easily from these data in the forced convection heat dissipation environment that the heat dissipation performance of the metal foam with composite cells is obviously better than that of the metal foam with spherical cells, and the control group is still the worst one.

4. Discussion

In the heat dissipation experiment, there are two main heat transfer modes—heat conduction and convection heat dissipation. In the first stage, heat transfer was first generated, and the heat was transmitted between the metal foam and the copper block, while in the second stage, the heat transfer was mainly achieved by convection heat dissipation.

For the first stage of heat transfer, according to Formula (A1) (Formula (A1) is presented in the Appendix A), the conduction of heat is proportional to the temperature gradient in this direction and the thermal conductivity, while the heat transfer direction is opposite to the temperature gradient direction. According to the figures of the temperature gradient, there is not much difference between the aluminium foam and the copper foam. Therefore, the heat conductivity will have a significant influence on heat conduction. In other words, the difference between the copper and the aluminium is shown in this experiment. It is well known that the thermal conductivity of aluminium and copper is 237 $\mathrm{W}/\left(\mathrm{m}·\mathrm{K}\right)$ and 401 $\mathrm{W}/\left(\mathrm{m}·\mathrm{K}\right)$ [24], respectively. In addition, the copper foam dissipates heat faster than the aluminium does in any case of this experiment, and this can also be seen in

Table 3. The temperature difference between the different metals in different ways ΔT*.

Mode of Convection	ΔT* (Al)	ΔT* (Cu)
Natural convection	9.375	10.775
Forced convection	12.6	16.725

ΔT* is the temperature at the end of the first stage minus the initial temperature.

.

In the later stage, it can be concluded from the test results that under the natural convection condition, the metal foam with different cell structures have similar heat dissipation effects, and the temperature dropped by about 31 °C. In addition, great differences between foam Al and Cu were not shown.

According to Formula (A2) (Formula (A2) is presented in the Appendix A), the convective heat dissipation performance of metal foam is mainly affected by the contact area between the air and the wall, the temperature difference, and the heat transfer coefficient of air. In the natural convection environment, the cooling process results in thermal convection with the air, which becomes the main factor. It is well known that the natural convective heat transfer coefficient of air is low: the coefficient is $1~10 \mathrm{W}/\left({\mathrm{m}}^2·\mathrm{K}\right)$ [25]. Hence, the temperature of the aluminium foam and the foam copper decreased by basically the same amount, even with different cell structures. At the same time, the control group with a smooth surface, and the cooling surface area was far smaller than that of the metal foam, thus, they showed poor heat dissipation performance, and even so, it still aligns with the fundamental law of heat transfer (Formula (A1)). There was not a particularly big difference in the temperature gradient curve of the metal foam. Aiming at understanding this phenomenon, here are the following explanations: The great difference between the control group and the metal foam in the first stage is because the metal foam absorbed heat from the copper block at the bottom. While in the later stage, the heat was absorbed by the metal foam at its peak, so the control group had a similar tendency.

While under the condition of forced convection, the cooling performance of the spherical cell and the cell structure of the composite metal foam showed noticeable differences. In addition, it is worth noting that regardless of the spherical cell or composite cell structure, the copper foam showed an excellent heat dissipation performance.

For the condition of forced convection, the contact area between the air and the metal foam surface is less than that of the inner surface. In addition, the heat transfer coefficient of the air increased significantly: the coefficient is 20~100 $\mathrm{W}/\left({\mathrm{m}}^2·\mathrm{K}\right)$ [25], which leads to differences between the metals. Additionally, because Cu has a high thermal conductivity, the heat from the bottom copper block transferred more quickly to the copper foam in the first stage, which led to the wall temperature of the copper foam rising fast. Hence, the difference between the temperature of the surface and airflow is considerable, according to Formula (A1), and the metal foam which has a big temperature difference has large heat transfer and fast heat loss values, so the copper foam showed a better heat dissipation performance.

Aiming at understanding the influence of the cell structure on the heat dissipation performance, the spherical cell has no big connection between the cells. There are only a few connected windows, shown in Figure 10, which are caused by the space holders coming into contact with each other under pressure. Therefore, they have less contact with the air, showing a relatively weak heat dissipation performance. For the composite cells structure, due to the existence of a large number of hexagonal channels, the contact area between the air and the cell wall increased, as shown in Figure 11. Therefore, it has a high through-cell rate and a large specific surface area, so the air through the metal foam had a large heat exchange area [26]. Therefore, it showed an excellent heat dissipation performance.

As for the absolute temperature gradient, the composite cells metal foam was more significant than the spherical cell metal foam and the control group were. That is to say, the temperature of the composite cells metal foam dropped faster.

Taking advantage of this characteristic, metal foam can be used as a suitable heat dissipation device. It is usually applied to a heat source that continuously generates heat, such as a CPU. However, the heat dissipation environment built in this experiment ignored this point. To better fit the actual environment, the heat dissipation model must be partially improved in subsequent studies. Even so, this experiment can conclude that metal foam can improve the heat dissipation performance of the system. In the natural convection heat dissipation test, the composite cell metal foam showed similar heat dissipation performances to the spherical cell. In the forced convection heat dissipation test, the composite cell metal foam had a better heat dissipation performance.

5. Conclusions

• Using Na₂S₂O₃·5H₂O as the space holder, the metal foams with controllable porosity and a porous structure can be successfully prepared. In addition, this method has broad application prospects in the preparation of other high-melting foams such as titanium, iron, nickel, etc.;
• In the environment of natural convection heat transfer, the metal foam can only slightly improve the heat dissipation of the system. However, there is little difference between the metal foam with different cell structures. In addition, the metal type has little effect on the heat dissipation performance;
• In the forced convection heat transfer environment, the metal foam shows a better heat dissipation performance, and the difference between the metal foams can be revealed. Metal foam with a composite cell structure has a better heat dissipation performance, while copper foam has a better heat dissipation performance than aluminium foam does.